Press n or j to go to the next uncovered block, b, p or k for the previous block.
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* @license Apache-2.0
*
* Copyright (c) 2026 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/* eslint-disable max-len, max-params */
'use strict';
// MODULES //
var max = require( '@stdlib/math/base/special/max' );
var min = require( '@stdlib/math/base/special/min' );
var floor = require( '@stdlib/math/base/special/floor' );
var dorglq = require( './dorglq.js' );
var dorgqr = require( './dorgqr.js' );
// MAIN //
/**
* Generates one of the real orthogonal matrices `Q` or `P^T` determined by `DGEBRD` when reducing a real matrix `A` to bi-diagonal form: `A = Q * B * P^T`.
*
* ## Notes
*
* - `Q` and `P^T` are defined as products of elementary reflectors `H(i)` or `G(i)` respectively.
*
* - If `vect = 'Q'`,
*
* - A is assumed to have been an M-by-K matrix, and Q is of order M.
* - if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n columns of Q, where m >= n >= k;
* - if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an M-by-M matrix.
*
* - If `vect = 'P'`,
*
* - A is assumed to have been a K-by-N matrix, and P**T is of order N
* - if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m rows of P**T, where n >= m >= k
* - if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as an N-by-N matrix.
*
* - LWORK >= max(1,min(M,N)). For optimum performance LWORK >= min(M,N)*NB, where NB is the optimal blocksize.
*
* - If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array
*
* @private
* @param {string} vect - specifies whether the matrix Q or the matrix P**T is returned in `A`
* @param {NonNegativeInteger} M - number of rows of `Q` or `P^T`
* @param {NonNegativeInteger} N - number of columns of `Q` or `P^T`
* @param {NonNegativeInteger} K - number of elementary reflectors
* @param {Float64Array} A - input/output matrix
* @param {integer} strideA1 - stride length of the first dimension of `A`
* @param {integer} strideA2 - stride length of the second dimension of `A`
* @param {NonNegativeInteger} offsetA - starting index for `A`
* @param {Float64Array} TAU - scalar factors of elementary reflectors
* @param {integer} strideTAU - stride length of `TAU`
* @param {NonNegativeInteger} offsetTAU - starting index for `TAU`
* @param {Float64Array} WORK - workspace array
* @param {integer} strideWORK - stride length of `WORK`
* @param {NonNegativeInteger} offsetWORK - starting index for `WORK`
* @param {NonNegativeInteger} LWORK - dimension of the array `WORK`
* @returns {integer} status code
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 1, 0, 0, -1, -2, 0 ] );
* var TAU = new Float64Array( [ 1, 1 ] );
* var WORK = new Float64Array( 10 );
*
* var info = dorgbr( `P`, 2, 3, 2, A, 1, 2, 0, TAU, 1, 0, WORK, 1, 0, 10 );
* // A => <Float64Array>[ 0, 0, 0, 0, 2, 0 ]
* // info => 0
* // WORK[ 0 ] => 96
*/
function dorgbr( vect, M, N, K, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, LWORK ) {
var lquery;
var lwkopt;
var wantq;
var mn;
var i;
var j;
wantq = ( vect === 'Q' );
mn = min( M, N );
lquery = ( LWORK === -1 );
WORK[ offsetWORK ] = 1;
if ( wantq ) {
if ( M >= K ) {
dorgqr( M, N, K, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, -1 );
} else if ( M > 1 ) {
dorgqr( M - 1, M - 1, M - 1, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, -1 );
}
} else if ( K < N ) {
dorglq( M, N, K, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, -1 );
} else if ( N > 1 ) {
dorglq( N - 1, N - 1, N - 1, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, -1 );
}
lwkopt = floor( WORK[ offsetWORK ] );
lwkopt = max( lwkopt, mn );
if ( lquery ) {
WORK[ offsetWORK ] = lwkopt;
return 0;
}
if ( M === 0 || N === 0 ) {
WORK[ offsetWORK ] = 1;
return 0;
}
if ( wantq ) {
// Form Q, determined by a call to DGEBRD to reduce an `M-by-K` matrix...
if ( M >= K ) {
// If M >= K, assume M >= N >= K:
dorgqr( M, N, K, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, LWORK );
} else {
// If M < K, assume M = N; Shift the vectors which define the elementary reflectors one column to the right, and set the first row and column of Q to those of the unit matrix...
for ( j = M - 1; j >= 1; j-- ) {
A[ offsetA + ( j * strideA2 ) ] = 0.0;
for ( i = j + 1; i < M; i++ ) {
A[ offsetA + ( i * strideA1 ) + ( j * strideA2 ) ] = A[ offsetA + ( i * strideA1 ) + ( ( j - 1 ) * strideA2 ) ];
}
}
A[ offsetA ] = 1.0;
for ( i = 1; i < M; i++ ) {
A[ offsetA + ( i * strideA1 ) ] = 0.0;
}
if ( M > 1 ) {
// Form Q(2:m,2:m):
dorgqr( M - 1, M - 1, M - 1, A, strideA1, strideA2, offsetA + strideA1 + strideA2, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, LWORK );
}
}
} else if ( K < N ) {
// If k < n, assume k <= m <= n:
dorglq( M, N, K, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, LWORK );
} else {
// If k >= n, assume m = n; Shift the vectors which define the elementary reflectors one row downward, and set the first row and column of P**T to those of the unit matrix...
A[ offsetA ] = 1.0;
for ( i = 1; i < N; i++ ) {
A[ offsetA + ( i * strideA1 ) ] = 0.0;
}
for ( j = 1; j < N; j++ ) {
for ( i = j - 1; i >= 1; i-- ) {
A[ offsetA + ( i * strideA1 ) + ( j * strideA2 ) ] = A[ offsetA + ( ( i - 1 ) * strideA1 ) + ( j * strideA2 ) ];
}
// A(0, j) = 0
A[ offsetA + ( j * strideA2 ) ] = 0.0;
}
if ( N > 1 ) {
// Form P**T(2:n,2:n)
dorglq( N - 1, N - 1, N - 1, A, strideA1, strideA2, offsetA + strideA1 + strideA2, TAU, strideTAU, offsetTAU, WORK, strideWORK, offsetWORK, LWORK );
}
}
WORK[ offsetWORK ] = lwkopt;
return 0;
}
// EXPORTS //
module.exports = dorgbr;
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